Hi everyone, I need a step-by-step solution for this calculus optimization problem:

"A farmer has 2,400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?"

Please show all your work clearly, including setting up the area function, taking the derivative, and using the first derivative test to verify the maximum.

Thank you so much for your help!